Theorems · Theorem · category theory
ComplexShape.quotient_isLocalization
∀ {ι : Type u_1} (c : ComplexShape ι),
(∀ (j : ι), ∃ i, c.Rel i j) →
∀ (C : Type u_2) [inst : CategoryTheory.Category.{v_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
[CategoryTheory.Limits.HasBinaryBiproducts C],
(HomotopyCategory.quotient C c).IsLocalization (HomologicalComplex.homotopyEquivalences C c)- Defined in
- Mathlib.Algebra.Homology.Localization
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HomologicalComplexstatement · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- ComplexShape.Relstatement and proof · cited by 518
- CategoryTheory.Functor.IsLocalizationstatement · cited by 432
- CategoryTheory.Limits.HasBinaryBiproductsstatement and proof · cited by 165
- HomotopyCategorystatement and proof · cited by 132
- HomotopyCategory.quotientstatement and proof · cited by 109
- CategoryTheory.MorphismProperty.Localizationproof · cited by 72
- HomologicalComplex.homotopyEquivalencesstatement and proof · cited by 22
- CategoryTheory.Functor.IsLocalization.mk'proof · cited by 6
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